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Résumé |
Krylov complexity is finding its way into areas of physics ranging from many-body chaotic dynamics to quantum gravity. In this talk I will give an overview of some recent results, both of interest to many-body physicists and holographers. In particular, I will develop a classical counterpart of the Krylov complexity framework by running the Lanczos algorithm directly on the algebra of observables of a classical Hamiltonian system. I will show that this construction arises naturally as the semiclassical limit of the quantum Lanczos algorithm. We demonstrate the usefulness of classical Krylov complexity in characterisation early-time dynamics in chaotic quantum systems with a semiclassical limit, and derive a Krylov-Ehrenfest theorem, which captures the eventual divergence of semiclassical and exact Krylov dynamics |
